用plotly画一张图,要求是一段空间曲线,然后在其中的某一点,标注出该点的切向量,主法向量和副法向量
时间: 2024-03-30 22:35:53 浏览: 97
一个关于画曲线的程序
好的,我可以帮您用Plotly画一张这样的图。以下是示例代码:
```python
import plotly.graph_objects as go
import numpy as np
# 生成曲线上的点
t = np.linspace(0, 2 * np.pi, 1000)
x = np.sin(t)
y = np.cos(t)
z = t
# 计算切向量、主法向量和副法向量
dx_dt = np.cos(t)
dy_dt = -np.sin(t)
dz_dt = np.ones_like(t)
dr_dt = np.array([dx_dt, dy_dt, dz_dt])
dr_dt_norm = np.linalg.norm(dr_dt, axis=0)
tangent_vector = dr_dt / dr_dt_norm
d2x_dt2 = -np.sin(t)
d2y_dt2 = -np.cos(t)
d2z_dt2 = np.zeros_like(t)
d2r_dt2 = np.array([d2x_dt2, d2y_dt2, d2z_dt2])
d2r_dt2_norm = np.linalg.norm(d2r_dt2, axis=0)
normal_vector = d2r_dt2 / d2r_dt2_norm
binormal_vector = np.cross(tangent_vector, normal_vector)
# 绘制曲线和向量
fig = go.Figure()
fig.add_trace(go.Scatter3d(
x=x, y=y, z=z,
mode='lines',
name='Curve',
))
point_of_interest = 500 # 选取曲线上的一个点
fig.add_trace(go.Scatter3d(
x=[x[point_of_interest]], y=[y[point_of_interest]], z=[z[point_of_interest]],
mode='markers',
name='Point of Interest',
))
# 在该点处绘制切向量、主法向量和副法向量
vector_scale = 0.25 # 向量缩放比例
vector_color = ['red', 'green', 'blue'] # 向量颜色
for vector, color, name in zip([tangent_vector[:, point_of_interest], normal_vector[:, point_of_interest], binormal_vector[:, point_of_interest]], vector_color, ['Tangent Vector', 'Normal Vector', 'Binormal Vector']):
fig.add_trace(go.Cone(
x=[x[point_of_interest]], y=[y[point_of_interest]], z=[z[point_of_interest]],
u=[vector[0] * vector_scale], v=[vector[1] * vector_scale], w=[vector[2] * vector_scale],
sizemode='absolute',
sizeref=0.1,
anchor='tail',
showscale=False,
colorscale=[[0, color], [1, color]],
name=name,
))
fig.update_layout(
scene=dict(
xaxis=dict(title='X'),
yaxis=dict(title='Y'),
zaxis=dict(title='Z'),
aspectratio=dict(x=1, y=1, z=0.3),
camera=dict(
eye=dict(x=-1.7, y=-1.7, z=0.5),
up=dict(x=0, y=0, z=1),
),
),
margin=dict(l=0, r=0, t=0, b=0),
)
fig.show()
```
这个代码会生成一个空间曲线,以及在曲线上的某个点处标注出其切向量、主法向量和副法向量。您可以根据需要修改点的位置、曲线的形状等参数。
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